Did you use water based? I used that a few years ago on the banister rails and it just peeled. Had to start again with oil based paint.
Other thing is that did you follow the normal steps? Sand very well, primer, undercoat then top coats? Any of those not done well, esp sanding will result in paint not adhering properly, esp obvious in something that gets a lot of wear and tear, like staircases.
Even if you sand it down to bare woodwork, use the correct primer, undercoat and gloss, you will find that the paint will chip because its a hardwood,
Thats why they are varnish stained,
Ah, am afraid that's your answer. I did get good results doing it the way I said, but as bosswhite mentioned, my other half knocked over a bookcase and it chipped a few bits upstairs and I've got to do it again. Mind you, was a very hard knock!
When painting previously painted wood whether its soft wood or hard wood, you need an adhesion primer first. Zinsser Coverstain probably the best. This can also be used with water based top coats or oil based.
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